INVESTIGATION OF PORE PRESSURE ON BURIED PIPELINES DUE TO THAWING OF SATURATED FROZEN SOIL

Transcription

1 INVESTIGATION OF PORE PRESSURE ON BURIED PIPELINES DUE TO THAWING OF SATURATED FROZEN SOIL * Hosein Razavi 1 and Ali Sanaei Rad 2 1 Department of Civil Engineering, College of Engineering, Khomein Branch, Islamic Azad University, Khomein, Iran 2 Department of Civil Engineering, Arak University, Iran *Author for Correspondence ABSTRACT Thaw of a frozen soil is controlled by boundary conditions and soil thermal properties. Frozen soils have substantially reduced permeability and the melting water in the thaw front cannot drain through the stillfrozen soil. Consequently, temporary excess pore-pressure is generated in the process which degrades the shear strength of the soil. This will ultimately reduce the bearing capacity in soils. In this paper, analytical solutions and a finite element method are used to estimate the thawing rate of frozen soils, in which a very good agreement is obtained for one-dimensional thawing. Axisymmetric geometry was used in Abacus to model the soil layers with a sinusoidal surface temperature. From the numerical simulation, it was obtained that a constant rate of thawing can be assumed for frozen soil layers for one directional topbottom thawing. The excess pore-water pressure largely depends on the initial ground temperature as well as on the magnitude of surface temperature. Keywords: Buried Pipe, Pore Pressure, Temperature, Thawing Rate INTRODUCTION Climate condition is one of the factors that affect design and performance of buried pipelines. Especially in cold regions, seasonal freezing and thawing process may occur in soil layers. The extent of damage on the soil layers due to freezing and subsequent thawing of subgrade soils depends on many factors such as the thermal gradient, availability of water in the sub-soil layers, frost susceptibility of the soil, consolidation coefficient, permeability and drainage conditions. If the rate of generation of water exceeds the discharge capacity of the soil, excess pore pressure will develop, which can lead to failure of foundations and slopes (Morgenstern and Nixon, 1971) and buried pipe. A soil structure will be most susceptible to breakup during the period when excess water cannot drain downward through still-frozen soil. A major practical aspect of predicting the thawing mechanism can be for effective buried pipelines. When the bound soil layer is thinner, the anticipated traffic load in the subgrade is high. Consequently, the excess pore water pressure(in the short term) during thawing increases, partly due to the phase change from the ice state, and partly due to the additional load such as the traffic.it showed that the excess porewater pressure developed during the spring thaw was the primary reason for the reduced bearing capacity. Pore water pressures of up to 0.90m above the drainage level was registered during thawing. The problem of spring thawing has no exact solution. Analytical solutions for heat conduction are well known and are obtained from the Newman s solution (Carslaw and Jaeger, 1959). Nixon (1973) formulated an approximated analytical solution from the theory of consolidation and principle of heat conduction for the development of excess pore water pressure following the thawing process. This analytical solution is valid for thawing of soils over thick ice layers. The impact of seasonal frost penetration on pavement has been widely studied, with considerably less focus on thaw weakening from thawing (Simonsen and Isacsson, 1999). This paper discusses on the rate of thawing (thaw advancement) in the frozen soil layers on buried pipelines and the subsequent excess pore water pressure. The study is based on the existing analytical solutions and finite element method (FEM). The general FEM program, Abaqus has been used to model the thawing process. The thawing process is widely understood qualitatively. For example, the types of soil layers that are frost susceptible are well known (Johnson et al., 1986; NPRA, 2011) and some empirical correlations exist relating the depth of frost penetration to the Copyright 2014 Centre for Info Bio Technology (CIBTech) 4184

2 Freezing Index (Andersland and Ladanyi, 2004). The study presented here focuses on the quantitative explanation of the thawing process based on the thermal properties of soil materials and thermal boundary conditions. With a better understanding of the thawing process, optimization process can be carried out during the design phase. Thermal Properties of Soils The principle of heat transfer in frozen soils is governed by conduction. The heat transfer process by convection is also minimal for fine-grained soils with very low permeability. During freezing, some of the water film is removed and ice crystals partially fill the voids between soil particles. This reduces the conductivity path for soil with low moisture content. In the contrary, experimental tests at high moisture content and densities showed increased conductivities in the frozen state, since ice fills the pores completely (Becker et al., 1992; Penner et al., 1975). The thermal conductivity of ice is more than four times greater than that of water (Penner, 1970). In the thawing process of frozen soils, the amount of water in the frozen state plays a significant role in the development of pore water pressure. Some assumptions are made in the analyses in this paper such as the frozen soil is fully saturated, the heat transfer mechanism is only by conduction, and the thermal conductivity of the soil is isotropic. Analytical and Numerical Solutions for the Thawing Process Nixon and McRoberts (1973) studied on the thawing rate of homogeneous frozen soil subjected to a step increase in temperature from (Tg) in the ground to (Ts) at the surface. The analytical formula relating the depth of thawing to the square root of time, based on Newman s solution (Carslaw and Jaeger, 1959) is shown in Eq. 1. x = a (1 Where X is the depth of thaw, t is the time and equation.α is a constant determined from Newman s rigorous When the ground temperature is close to zero, the equation from Newmann is simplified as (Nixon and McRoberts 1973); Where α is the constant in Eq. 1. is the thermal conductivity of unfrozen is the volumetric heat capacity of unfrozen L is the volumetric latent heat of the soil is the applied constant surface temperature ( C) Finite Element Analysis In the thawing process, temperature has a direct effect on the water flow field in saturated and unsaturated soils which undergo drainage and consolidation upon thawing. Figure 1: Specific heat, latent heat definition (Abaqus, 2011) Copyright 2014 Centre for Info Bio Technology (CIBTech) 4185

3 As a result of this, the heat flow and fluid flow equations are coupled mathematically through the phase change component and an optimization procedure is incorporated into the computational scheme (Harlen, 1973). In a saturated soil, the latent heat absorbed/released on the thaw-freeze front has a major impact on the rate of thawing. In the numerical scheme, the latent heat can be defined in two ways (Xu et al., 2009). It can be included in the heat conduction equations or it can be defined by using temperature dependent specific heat as shown in Figure (1). In this analysis, the latent heat is assumed to be released between-0.1 0C and 0. Thermal properties of the soil, listed in Table (1) are used both for the analytical analysis and numerical simulation. For the numerical input, temperature dependent thermal thawed states. A frozen soil is almost impermeable and a very low permeability properties are used for the frozen and K = 1, is used for the ground temperature less than zero degree Celsius. Table 1: Input parameters Parameters Thaw conductivity Consolidation coefficient ( C u ) Permeability ( k ) Unit weight ( ) Latent heat of soil ( volumetric ) Latent heat of water Surface temperature Ground tempereture Unit Value The conductivity of the frozen soil is assumed to be twice that of the thawed soil. Similarly, the stiffness of the frozen soil is assumed to be 100 times that of the stiffness in the thawed state. The amount of frozen water is directly related to the moisture content. For fully saturated soils, a reasonable assumption of void ratio can be made from the following relationship. e = Where e is the void ratio, w is the water content, Gs is the specific gravity of the soil, and S is the degree of saturation, ( S= 1 for fully saturated condition). In reality, the void ratio of soils varies greatly upon freezing and thawing. The permeability of the soil can be defined as a function of void ratio in the numerical simulation. Figure 2: Comparison of analytical solution and numerical simulation The stiffness of the thawed soil in the numerical analysis is determined from Poisson s ratio and the modulus which is related to the coefficient of consolidation (Janbu, 1970; Berntsen, 1993). Some variables for predefined fields in Abaqus are defined. The initial pore water pressure is set to zero. The initial temperature of the frozen soil (ground temperature) in assumed to be zero to compare the results with the simplified Neumann s solution in Eq. 2.The soil is also considered to be fully saturated Copyright 2014 Centre for Info Bio Technology (CIBTech) 4186

4 prior to thawing. Detailed procedures for defining predefined fields, initial conditions, and thermal boundary conditions are available in the Abaqus FEA. The analytical solution from (Eq. 2) has been compared with the result obtained from a numerical analysis using axisymmetric geometry and coupled temperature-pore pressure elements in Abaqus. The thawing depth from the numerical simulation is obtained by plotting the time at which the temperature is changed from negative to positive ( ) at selected nodes in the frozen soil layer. A very good agreement is obtained from the analytical solution and numerical simulation (see Figure 2). Excess Pore-Water Pressure One of the consequences of thawing is generated excess pore water that it depending on the overburden stress from the soil layers and external loading from the traffic. In the case where a thick ice layer exists, an excess pore water pressure can develop even from self-weight loading of the soil on the ice layer. This phenomenon was modeled analytically by Nixon (1973). The analysis is based on the principle of heat conduction and Terzaghi s one-dimensional consolidation theory. From the coupled numerical analysis (using Abaqus), it is possible to obtained excess-pore water pressure. The amount of excess pore water pressure is very sensitive the volumetric thermal expansion of pore water in the voids of the frozen soil and the stiffness of the frozen soil. So, a direct consideration of the output from the numerical analysis may be misleading. Since we can accurately predict the advancement of thawing by using the numerical analysis, we can relate the development of excess pore water to the thawing rate. A hydrostatic pore water pressure can be assumed for a thawed soil if no additional loading exists. For example, for a frozen soil layer under a loading, the excess pore water pressure will be the total overburden pressure (asphalt, base and other layers) including the loading from the traffic. This assumption is valid for untrained conditions. In many cases, frozen materials (aggregates) facilitate the dissipation of excess pore water pressure. Then, post-thaw consolidation follows. Detail analysis of one-dimensional thaw consolidation is presented in Morgenstern and Nixon (1971). Modeling of Thawing Soil Layers on Buried Pipelines Most of the analytical solutions available in the literature for the thawing process are based on a one step temperature increment on the surface. In reality, the change of surface temperature is neither a step change nor constant. It is closer to a sinusoidal curve. An advantage is gained by using numerical analysis for different boundary conditions and sol layers. An axisymmetric geometry is modeled in Abaqus as shown in Figure 3. This modeling (geometrically) is a reasonable approximation for isotropic behavior of pavement materials and an efficient computation time is obtained for the numerical thermal analysis. The assumed thermal properties of the asphalt materials and base course are listed in Table 2. The frozen subgrade is modeled in the same way described in section 2.1. A sinusoidal surface temperature is considered based on a local weather data. Figure 3: Numerical model Copyright 2014 Centre for Info Bio Technology (CIBTech) 4187

5 Table 2: Thermal properties of the Asphalt and base layers Value Parameters Unit Asphalt Conductivity 0.75 Specific heat 920 Coefficient of expansion Base - course Assuming a uniform initial ground temperature Tg=-5 C the temperature distribution in the frozen subgrade due to the change of surface temperature on the pavement surface and initial temperature in the steel buried pipe assumed 11 C. It is noted that it takes about 90 days for the frozen layer to start thawing from the time since the surface temperature has been greater than 0 C. Full scale field tests (Nordal and Hansen, 1987) showed a time period of 70 days for the temperature measurement at 1.93m below the pavement surface for the subgrade soil temperature to be changed from negative to positive temperature(in degree celcius). Nordal and Hansen measured the temperature variations at at depth of 0.05m, 0.15m, 0.63m, 0.93m and 1.93m. The measurements showed that the surface temperature is higher than the data used in our numerical analysis. In accounting this fact, the approximation obtained from the numerical analysis can be accounted for practical case studies. The analytical solutions for temperature distributions (for example Stephan s formula) relate the thawing depth to be proportional to the square root of time of thawing. Based on the results from the FEM analysis, when sinusoidal surface temperature and thermal properties of pavement layers such as asphalt and base layers are considered, the thawing depth can be directly proportional to the rate time (see Figure 4). Figure 4: Thawing rate in frozen subgrade under a pavement An average of 110 days is required for the frozen layer to start thawing for the given thermal properties and boundary conditions assumed in this analysis. No significant difference is observed for the variation of the initial ground temperature on the thaw rate. Constant rate of thawing in subgrades (in terms of mm/day) has been observed in different field tests reported in Dore (2004). Figure 5: Excess pore pressure at soil-ice interface for a constant surface temperature. The curves are based on the analytical solution of Nixon (1973) Copyright 2014 Centre for Info Bio Technology (CIBTech) 4188

6 It can be observed (in Figure 5) from analytical solution of Nixon (1973) that the time required for the development of maximum excess pore water pressure at the soil-ice interface (thawing period) is the same regardless of the temperature gradient. In the contrary, the maximum excess pore water pressure generated when the surface temperature is 30 C, is twice the maximum excess pore pressure generated at a constant surface temperature of 10 C. This comparison is only for self-weight loading of the soil and the expected excess pore water pressure can be very high depending on the overburden pressure from the pavements and traffic loading. Conclusion In the previous analytical methods of thaw depth calculations, the Stephan s method is commonly used and the thaw depth is assumed to be proportional to the square root of the thawing time. This assumption is valid for constant surface temperature based on a sinusoidal surface temperature has shown that for the case of frozen layers in pavements, a constant rate of thawing is obtained. A higher thawing rate in less permeable frozen soils results in high excess pore water pressure. The late spring thawing can be predicted from the change in pavement temperature from available climatic data, and thermal and physical properties of the pavement materials. This has a significant importance in buried pipe design and maintenance planning in cold climate regions. The development of excess pore water pressure highly depends on the temperature distribution in the soil layers and traffic load and initial states. The excess pore water pressure development is also largely dependent on the physical properties of the thawed soil such as the coefficient of consolidation and permeability. AKNOWLEDGEMENT The research is carried out at the khomin branch REFERENCES Abaqus FEA and Simulia DS (2011). Dassault Systèmes. Andersland OB and Ladanyi B (2004). Frozen Ground Engineering, 2nd edition. The American Society of Civil Engineers (John Wiley & Sons, Inc.). Becker BR, Misra A and Fricke BA (1992). Development of Correlations for Soil Thermal Conductivity. International Communications in Heat and Mass Transfer 19(1) Carslaw HS and Jaeger JC (1959). Conduction of Heat in Solids, 2nd edition (Oxford University Press). Berntsen G (1993). Reduction of bearing capacity during thawing (in Norwegian), Norwegian Institute of Technology: Trondheim, Norway. Doré G (2004). Development and validation of the thaw-weakening index. International Journal of Pavement Engineering 5(4) Harlan RL (1973). Analysis of Coupled Heat - Fluid Transport in Partially Frozen Soil. Water Resources Research 9(5) Janbu N (1970). Grunnlag i geoteknikk (in Norwegian). Trondheim: Tapir Forlag. Johnson TC, Berg RL, Chamberlain EJ and Cole DM (1986). Frost Action Predictive Techniques for Roads and Airfields: A Comprehensive Survey of Research Findings. Cold Regions Research and Engineering Laboratory CRREL report Morgenstern NR and Nixon JF (1971). One-dimensional consolidation of thawing soils. Canadian Geotechnical Journal 8(4) Nixon JF (1973). Thaw-Consolidation of Some Layered Systems. Canadian Geotechnical Journal 10(4) Nixon JF and McRoberts EC (1973). A study of some factors affecting the thawing of frozen soils. Canadian Geotechnical Journal 10(3) NPRA (2011). Handbook 018: Road construction standards (in Norwegian). Norwegian Public Roads Adminstration. Nordal RS and Hansen EK (1987). The Vormsund Test Road, Part 4: Summary report, Norwegian Road Research Laboratory. Copyright 2014 Centre for Info Bio Technology (CIBTech) 4189

7 Penner E (1970). Thermal Conductivity of Frozen Soils. Canadian Journal of Earth Science 7(3) Penner E, Johnston GH and Goodrich LE (1975). Thermal Conductivity Laboratory Studies of Some Mackenzie Highway Soils. Canadian Geotechnical Journal 12(3) Simonsen E and Isacsson U (1999). Thaw weakening of pavement structures in cold regions. Cold Regions Science and Technology 29(2) Xu J, Abdella B, Eltaher A and Jukes P (2009). Permafrost Thawing - Pipeline Interaction Advanced Finite Element Model. In Proceedings of the ASME th International Conference on Ocean, Offshore and Arctic Engineering. OMAE (2009). Honolulu, Hawaii, USA 1-6. Penner E, Johnston GH and Goodrich LE (1975). Thermal Conductivity Laboratory Studies of Some Mackenzie Highway Soils. Canadian Geotechnical Journal 12(3) Simonsen E and Isacsson U (1999). Thaw weakening of pavement structures in cold regions. Cold Regions Science and Technology 29(2) Xu J, Abdella B, Eltaher A and Jukes P (2009). Permafrost Thawing - Pipeline Interaction Advanced Finite Element Model. In Proceedings of the ASME th International Conference on Ocean, Offshore and Arctic Engineering, OMAE2009, Honolulu, Hawaii, USA, 1-6. Copyright 2014 Centre for Info Bio Technology (CIBTech) 4190